System and method for progressively transform coding digital data

ABSTRACT

The present invention is embodied in a system and method for compressing image data using a lapped biorthogonal transform (LBT). The present invention encodes data by generating coefficients using a hierarchical LBT, reorders the coefficients in a data-independent manner into groups of similar data, and encodes the reordered coefficients using adaptive run-length encoding. The hierarchical LBT computes multiresolution representations. The use of the LBT allows the present invention to encode image data in a single pass at any desired compression ratio and to make use of existing discrete cosine transform (DCT) software and hardware modules for fast processing and easy implementation.

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of U.S. patent applicationSer. No. 09/518,458, entitled “System and Method for ProgressivelyTransform Coding Digital Data,” filed Mar. 3, 2000, the entire contentsof which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention.

[0003] The present invention relates in general to processing digitaldata, and in particular, to a system and method for progressivelytransform coding image data using hierarchical lapped transforms forcompression of the image data.

[0004] 2. Related Art.

[0005] Digital images are widely used in several applications such as,for example, imaging software, digital cameras, Web pages and digitalencyclopedias. Usually it is necessary to compress the digital imagesdue to storage constraints and the desire to decrease access or downloadtime of the picture. Higher compression of a digital image means thatmore digital images can be stored on a memory device (such as diskette,hard drive or memory card) and these images can be transferred fasterover limited bandwidth transmission lines (such as telephone lines).Thus, efficient and effective compression of images is highly importantand desirable.

[0006] One of the most popular and widely used techniques of imagecompression is the Joint Photographic Experts Group (JPEG) standard. TheJPEG standard operates by mapping an 8×8 square block of pixels into thefrequency domain by using a discrete cosine transform (DCT).Coefficients obtained by the DCT are divided by a scale factor androunded to the nearest integer (a process known as quantizing) and thenmapped to a one-dimensional vector via a fixed zigzag scan pattern. Thisone-dimensional vector is encoded using a combination of run-lengthencoding and Huffman encoding.

[0007] Although JPEG is a popular and widely used compression technique,it has several disadvantages. For example, one disadvantage of JPEG isthat at low bit rates the DCT produces irregularities anddiscontinuities in a reconstructed image (known as tiling or blockingartifacts). Blocking artifacts cause the boundary between groups of 8×8blocks of pixels to become visible in the reconstructed image. Theseblocking artifacts cause an undesirable degradation in image quality.Another disadvantage of JPEG is that JPEG cannot perform imagereconstruction that is progressive in fidelity. In other words, if animage is encoded at a certain fidelity and a lower fidelity is laterdesired (for example, due to limited bandwidth or storage availability),the image must be decoded and re-encoded.

[0008] In order to overcome these shortcomings of JPEG, most modernimage compression techniques use a wavelet transform technique followedby a quantization and entropy encoding. Wavelet transform (WT) ispreferred over the DCT used in JPEG because WT does not have blockingartifacts and WT allows for image reconstruction that is progressive inresolution. Moreover, WT leads to better energy compaction and thusbetter distortion/rate performance than the DCT. WT-based compressionprovides compression ratios that typically are from 20% to 50% betterthan the JPEG standard. In fact, the performance of the WT over the DCTis so superior that all current compression techniques being consideredfor the JPEG-2000 standard use WT-based compression.

[0009] Most current WT-based compression techniques decompose an imageinto coefficients and use some form of entropy encoding (such asadaptive Huffman encoding or arithmetic encoding) of the coefficients tofurther compress the image. These types of encoding, however, can bequite complex and use, for example, complex symbol tables (such as inadaptive Huffman encoding) or complex data structures (such as zerotreedata structures) that depend on the data types. Thus, most currentWT-based techniques are complex and difficult to implement.

[0010] At least one type of WT-based compression techniques, aprogressive WT-based compression technique, includes the advantages ofnot requiring the use of data-dependent data structures (such aszerotrees) or complex symbol tables. This progressive WT-basedcompression uses entropy encoding of quantized wavelet coefficients andthen uses a simple data reordering structure to cluster most of thelarge and small wavelet coefficients into separate groups. Thisreordering of the wavelet coefficients is performed in a pattern that isdata-independent. Moreover, this progressive WT-based compressionencodes the bit planes of the reordered wavelet coefficients using anencoder that does not require complex symbol tables, such as, forexample, adaptive run-length and Rice-Golomb encoders. These featuresmake progressive WT-based compression simpler to implement than otherWT-based compression techniques, such as JPEG2000.

[0011] However, progressive WT-based compression still may be difficultto implement in some applications. In particular, DCT processing of 8×8pixel blocks (as used in the current JPEG standard, for example) hasbeen optimized in many software and hardware implementations, but is notused in WT-based compression. Thus, in order to implement progressiveWT-based compression, new software or new hardware modules must bedeveloped and installed to perform computation of the required wavelettransforms. This additional cost and time associated with implementationcan reduce the attractiveness of progressive WT-based compression.

[0012] Accordingly, there exists a need for a progressive imagecompression technique that is efficient, simple and easier to implementinto existing hardware and software. This progressive image compressiontechnique would retain the advantages of progressive WT-basedcompression and the JPEG compression standard without any of thedisadvantages. Specifically, this progressive image compressiontechnique would use the same 8×8 pixel blocks used in the JPEG standardbut would not produce blocking artifacts. This would allow theprogressive image compression technique to leverage existing JPEGhardware and software, therefore providing much simpler and inexpensiveimplementation than current WT-based compression techniques. Moreover,the progressive image compression would use data-independent reorderingstructures to further simplify implementation. Whatever the merits ofthe above-mentioned systems and methods, they do not achieve thebenefits of the present invention.

SUMMARY OF THE INVENTION

[0013] To overcome the limitations in the prior art as described aboveand other limitations that will become apparent upon reading andunderstanding the present specification, the present invention isembodied in a system and method for compressing image data using alapped biorthogonal transform (LBT). The present invention encodes databy generating coefficients using a hierarchical LBT, reorders thecoefficients in a data-independent manner into groups of similar data,and encodes the reordered coefficients using adaptive run-lengthencoding. The hierarchical LBT computes multiresolution representations.The use of the LBT allows the present invention to encode image data ina single pass at any desired compression ratio and to make use ofexisting discrete cosine transform (DCT) software and hardware modulesfor fast processing and easier implementation.

[0014] The present invention provides several advantages over currentJoint Photographic Experts Group (JPEG) and wavelet-based compressiontechnologies. In particular, unlike JPEG compression, the presentinvention does not produce blocking artifacts even though, in apreferred embodiment, the present invention uses 8×8 block discretecosine transform (DCT) as an intermediate step for computing LBT blocks.Moreover, the present invention does not use wavelets and is faster thanwavelet-based compression. The present invention does not use zerotreesor other data-dependent data structures, so that implementation of thepresent invention into hardware or software is simplified.

[0015] In general, the system of the present invention includes atransformation module, which generates transform coefficients using aLBT and a DCT, a quantization module, which approximates scaledcoefficients by integers, a reordering module, which reorders thecoefficients into groups of similar data, and an encoding module, whichuses adaptive run-length encoding to encode the reordered coefficients.The reordering module clusters most of the large and small coefficientsinto separate groups in a data-independent manner, so that zerotrees orother data-dependent data structures are not used. In a preferredembodiment, the encoding module encodes the reordered coefficients usingadaptive run-length and Rice-Golomb encoding.

[0016] The present invention also includes a method for compressingimage data using a hierarchical LBT. The method includes generating thecoefficients using the LBT transform followed by a DCT transform,quantizing scaled coefficients by approximating them by integers,reordering the coefficients to group the image data in adata-independent manner, and encoding the reordered coefficients usingadaptive run-length encoding. The present invention also includes amethod for decompressing a compressed bitstream by using adaptiverun-length decoding to obtain transform coefficients from the compressedbitstream, rearranging the coefficients into their original order, andusing an inverse DCT transform and an inverse LBT to obtain thereconstructed image data from the decoded coefficients.

[0017] Other aspects and advantages of the present invention as well asa more complete understanding thereof will become apparent from thefollowing detailed description, taken in conjunction with theaccompanying drawings, illustrating by way of example the principles ofthe invention. Moreover, it is intended that the scope of the inventionbe limited by the claims and not by the preceding summary or thefollowing detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Referring now to the drawings in which like reference numbersrepresent corresponding parts throughout:

[0019]FIG. 1 is a block diagram illustrating an apparatus for carryingout the invention.

[0020]FIG. 2 is a general block/flow diagram illustrating a system andmethod for encoding/decoding a signal in accordance with the presentinvention.

[0021]FIGS. 3A-3B are general block diagrams of encoders of the presentinvention.

[0022]FIGS. 4A-4B are general block diagrams of decoders related to theencoders of FIGS. 3A and 3B respectively, in accordance with the presentinvention.

[0023]FIG. 5A is a block diagram of the hierarchical lapped transform(HLT) processor of the present invention.

[0024]FIG. 5B is a block diagram of the LBT module of the HLT processorof FIG. 5A of the present invention.

[0025]FIG. 6 is a flow diagram of the hierarchical lapped transformprocessor of FIG. 5A the present invention.

[0026]FIG. 7 is a working example represented by a flow diagramillustrating the detailed operation of the components of thehierarchical lapped transform processor of FIG. 6.

[0027]FIG. 8 is the working example of FIG. 7 represented by a flowdiagram illustrating detailed operations and computations to derive thelapped biorthogonal operators of the hierarchical lapped transformprocessor of FIG. 7.

[0028]FIG. 9 is the working example of FIG. 7 represented by a blockdiagram illustrating reordered wavelet coefficients produced by thehierarchical lapped transform processor of FIG. 3A and FIG. 6.

[0029]FIG. 10 is a working example represented by a block diagramillustrating reordered HLT blocks produced by the block reorderingmodule of FIG. 3A.

[0030]FIG. 11 is a working example represented by a flow chart showingthe general operation of the lossless adaptive coefficient encoder ofFIG. 3A.

[0031]FIG. 12 is a working example represented by a flow chartillustrating further detail of the working example of the adaptiverun-length+Golomb-Rice encoder of FIGS. 11 and 3A.

[0032]FIG. 13 is a working example represented by a flow chartillustrating the writing of a matrix of coefficients in a reorderedmanner consistent with that shown in FIG. 10.

[0033]FIG. 14 is a simplified block diagram illustrating a real worldimplementation of the encoder of FIGS. 3A-3B and the decoder of FIGS.4A-4B in a software application environment that handles image data.

DETAILED DESCRIPTION OF THE INVENTION

[0034] In the following description of the invention, reference is madeto the accompanying drawings, which form a part hereof, and in which isshown by way of illustration a specific example in which the inventionmay be practiced. It is to be understood that other embodiments may beutilized and structural changes may be made without departing from thescope of the present invention.

[0035] I. Exemplary Operating Environment

[0036]FIG. 1 and the following discussion are intended to provide abrief, general description of a suitable computing environment in whichthe invention may be implemented. Although not required, the inventionwill be described in the general context of computer-executableinstructions, such as program modules, being executed by a personalcomputer. Generally, program modules include routines, programs,objects, components, data structures, etc. that perform particular tasksor implement particular abstract data types. Moreover, those skilled inthe art will appreciate that the invention may be practiced with othercomputer system configurations, including hand-held devices,multiprocessor systems, microprocessor-based or programmable consumerelectronics, network PCs, minicomputers, mainframe computers, and thelike. The invention may also be practiced in distributed computingenvironments where tasks are performed by remote processing devices thatare linked through a communications network. In a distributed computingenvironment, program modules may be located on both local and remotememory storage devices.

[0037] With reference to FIG. 1, an exemplary system for implementingthe invention includes a general-purpose computing device in the form ofa conventional personal computer 100, including a processing unit 102, asystem memory 104, and a system bus 106 that couples various systemcomponents including the system memory 104 to the processing unit 102.The system bus 106 may be any of several types of bus structuresincluding a memory bus or memory controller, a peripheral bus, and alocal bus using any of a variety of bus architectures. The system memoryincludes read only memory (ROM) 110 and random access memory (RAM) 112.A basic input/output system 114 (BIOS), containing the basic routinesthat help to transfer information between elements within the personalcomputer 100, such as during start-up, is stored in ROM 110. Thepersonal computer 100 further includes a hard disk drive 116 for readingfrom and writing to a hard disk, not shown, a magnetic disk drive 118for reading from or writing to a removable magnetic disk 120, and anoptical disk drive 122 for reading from or writing to a removableoptical disk 124 such as a CD ROM or other optical media. The hard diskdrive 116, magnetic disk drive 128, and optical disk drive 122 areconnected to the system bus 106 by a hard disk drive interface 126, amagnetic disk drive interface 128, and an optical drive interface 130,respectively. The drives and their associated computer-readable mediaprovide nonvolatile storage of computer readable instructions, datastructures, program modules and other data for the personal computer100. Although the exemplary environment described herein employs a harddisk, a removable magnetic disk 120 and a removable optical disk 124, itshould be appreciated by those skilled in the art that other types ofcomputer readable media which can store data that is accessible by acomputer, such as magnetic cassettes, flash memory cards, digital videodisks, Bernoulli cartridges, random access memories (RAMs), read onlymemories (ROM), and the like, may also be used in the exemplaryoperating environment.

[0038] A number of program modules may be stored on the hard disk,magnetic disk 120, optical disk 124, ROM 110 or RAM 112, including anoperating system 132, one or more application programs 134, otherprogram modules 136, and program data 138. A user may enter commands andinformation into the personal computer 100 through input devices such asa keyboard 140 and pointing device 142. Other input devices (not shown)may include a microphone, joystick, game pad, satellite dish, scanner,or the like. These and other input devices are often connected to theprocessing unit 102 through a serial port interface 144 that is coupledto the system bus 106, but may be connected by other interfaces, such asa parallel port, game port or a universal serial bus (USB). A monitor146 or other type of display device is also connected to the system bus106 via an interface, such as a video adapter 148. In addition to themonitor 146, personal computers typically include other peripheraloutput devices (not shown), such as speakers and printers.

[0039] The personal computer 100 may operate in a networked environmentusing logical connections to one or more remote computers, such as aremote computer 150. The remote computer 150 may be another personalcomputer, a server, a router, a network PC, a peer device or othercommon network node, and typically includes many or all of the elementsdescribed above relative to the personal computer 100, although only amemory storage device 152 has been illustrated in FIG. 1. The logicalconnections depicted in FIG. 1 include a local area network (LAN) 154and a wide area network (WAN) 156. Such networking environments arecommonplace in offices, enterprise-wide computer networks, intranets andInternet.

[0040] When used in a LAN networking environment, the personal computer100 is connected to the local network 154 through a network interface oradapter 158. When used in a WAN networking environment, the personalcomputer 100 typically includes a modem 160 or other means forestablishing communications over the wide area network 156, such as theInternet. The modem 160, which may be internal or external, is connectedto the system bus 106 via the serial port interface 144. In a networkedenvironment, program modules depicted relative to the personal computer100, or portions thereof, may be stored in the remote memory storagedevice. It will be appreciated that the network connections shown areexemplary and other means of establishing a communications link betweenthe computers may be used, such as a direct connection via an integratedservices digital network (ISDN) connection.

[0041] II. Introduction

[0042] The present invention is embodied in a system and method forprogressively transform coding image data using hierarchical lappedtransforms for compression of the image data. The present inventionallows progressive image reconstruction, both in resolution and infidelity, with a fully embedded bitstream. The present invention usesbit-plane entropy coding of reordered transform coefficients andperforms space-frequency decompositions with a lapped biorthogonaltransform (LBT). The present invention achieves a rate vs. distortionperformance that is comparable to current state-of-the-artcoders/decoders (codecs), such as SPIHT (set partitioning inhierarchical trees). However, the LBT of the present invention reducesthe number of multiplications and additions per pixel, when compared towavelet-based systems. Further, since most of the computations in theLBT is performed by a discrete cosine transform (DCT), the presentinvention can make full use of fast software and hardware modules forone-dimensional and two-dimensional DCTs that are currently being usedin many imaging systems.

[0043] III. General Overview

[0044]FIG. 2 is a general block/flow diagram illustrating a system andmethod for encoding/decoding a signal in accordance with the presentinvention. First, in general data 210, such as raw data bits in the formof image data, is received and processed by a hierarchical encoder 212and an adaptive entropy coder 214 to produce an encoded bitstream 215 inaccordance with the present invention (a detailed description of theencoder is provided below). The encoded bitstream 215 can be utilized inany desired manner, such as for storage or transmission (box 216) of theencoded bitstream 215. After utilization of the encoded bitstream 215,it can be sent to a digital decoder 218, which processes the encodedbitstream 215 with an inverse transformation to produce thereconstructed data 220. The reconstructed data output 220 of the decoder218 is a close approximation to the input data 210; a human eyeobserving the pictures represented by the data in 210 and 220 may notperceive any differences.

[0045] In particular, the hierarchical encoder 212 comprises a transformprocessor 230 and can include a reordering processor 232. The transformprocessor 230 preferably produces a hierarchical lapped transform. Thereordering processor 232 is preferably a coefficient and blockingprocessor that ensures certain combined coefficients represent a similarmapping between spatial domain and frequency domain as that obtainedwith a wavelet transform. In other words, this reordering makes thehierarchical lapped transform 230 a good approximation to a wavelettransform, to allow subsequent clustering of insignificant values. Theadaptive coder 214 is preferably an adaptive entropy coder that entropyencodes bit planes of quantized and reordered transform coefficientsproduced by the hierarchical encoder 212. These components can beimplemented with integrated circuits as computer hardware or withalgorithmic routines as computer software.

[0046] IV. Components

[0047]FIGS. 3A-3B are general block diagrams of encoders of the presentinvention. The hierarchical encoder 212 of FIG. 2 can be implemented ashierarchical encoder 312 of FIG. 3A or as hierarchical encoder 352 ofFIG. 3B for image pixel encoding, with corresponding decoders shown inFIGS. 4A and 4B, respectively. While the encoders and decoders aredescribed with respect to image pixel data as the respective input andoutput, it should be noted that other data can also be transformed asdesired.

[0048] In the embodiment shown in FIG. 3A, image pixel data 310 isprovided to a hierarchical lapped transform processor 312. Thehierarchical lapped transform processor 312 includes a lappedbiorthogonal transform (LBT) 330, a discrete cosine transform (DCT) 332and a coefficient reordering processor 334 to produce a hierarchicallapped transform. The LBT performs space-frequency decompositions andproduces transform coefficients from the original input. The DCT helpsincrease the compression performance by further transforming groups ofthe lowest frequency coefficients of the LBT blocks. The outputs of theDCT operator represent low-frequency variations of a large regions ofsupport, in a form analogous to the course resolution coefficients of awavelet transform. The coefficient reordering processor 334 ensurescombined LBT and DCT coefficients represent an appropriate mappingbetween the spatial domain and the frequency domain to ensure that thehierarchical lapped biorthogonal transform represents a goodapproximation to a wavelet transform. This allows subsequent clusteringof insignificant values by a block reordering processor 318 afterquantization of the hierarchical lapped biorthogonal transform byquantizer 314. One set of such grouping is shown in FIG. 9, for anexample with blocks with 64 coefficients.

[0049] Quantization can be performed by a uniform quantizer, which iscontrolled by a quantization step defining threshold T. This results inthe representation of each coefficient falling between the steps by thevalue in the middle of the step. The smaller T, the less loss isincurred in the quantization. Thus, the output of the quantizer 314 is aseries of integer numbers, which are quantized coefficients. As in manyother applications, the quantizer may be based on normal rounding, or inrounding towards zero (also known as a quantizer with a “dead zone”).

[0050] The block reordering processor 318 groups coefficients intoclusters of like values. It results in a clustering or grouping togetherof the blocks of frequency coefficients, which are most likely to bezero. The reordering increases the likelihood of groupings of similardata, in the sense that the data tends to have approximatelymonotonically decaying distribution of amplitudes. The first blocks tendto have data of larger amplitude, whereas in subsequent blocks theamplitudes of the coefficients tend to decay. The grouping is done byfixing a scanning order, which is data independent. One set of suchgrouping is shown in FIG. 10, for an example with 64 blocks ofcoefficients. In FIG. 10, low frequency components are placed toward theupper left corner of the grouping with an alternation of blocks ofcoefficients from low-high and high-low subbands at each level and isdiscussed in detail below.

[0051] An adaptive encoding block 320 receives the macroblocks andencodes them in a lossless manner to produce an encoded bitstream 322.The clustering of the blocks provide data to compress, which has largeclusters of zeros. Further reordering the data by encoding on a bitplane basis increases the likelihood of finding large strings of zeros.Starting with the most significant bit for the first bit plane leads toa higher likelihood of long strings of zeros. Further, this also ensuresthat the most relevant data is encoded first. By the time the third orfourth bit planes are encoded, the odds are about equal for a zero asopposed to a one, and straight binary encoding may be effectively used.

[0052] The encoder 320 is preferably an adaptation of a Golomb-Riceencoder with adaptive run-length modifications. In simple terms, astring of 2^(k) zeros is represented by the codeword consisting of asingle bit equal to zero. The length of the string of zeros representedby the zero codeword is controlled by the parameter k, which is variedas data is encountered, based on the observed frequency of zeros. When azero value is encoded, it is assumed that zeros are more likely, and sothe value of the parameter k is increased. When a nonzero value isencountered, k is decreased. By controlling the amount of such increaseand decrease appropriately, the encoder can track well a string of bitswith a varying probability of zero, without the need of the overhead ofactually estimating that probability.

[0053] A feedback loop 324 is used to represent the backwards adaptivenature of the encoder 320. This encoding provides for efficientcompression and fast adaptation to changes in the statistics of theincoming data. Encoder 320 provides a bitstream output that isinherently progressive, in that the most relevant information isprovided at the beginning of the bitstream. Since the least significantbits are encoded in the last bit plane, for lower resolution bitstreams,they may effectively be discarded or not encoded. This is useful forlower bandwidth transmissions of data. This scalability control bydiscarding of least significant bit planes, wholly or in part, can beperformed by the encoder itself or by any element of a communication orstorage system, in order to produce a lower fidelity representation ofthe data. For example, if the data is to be transmitted through theInternet, a server or router may parse the encoded bitstream to decidehow many bit planes can be transmitted to a particular decoder client.In another example, if a memory management module in a digital cameraneeds more memory space for an additional picture, it can removebitplanes from previously shot pictures to generate such space.

[0054] The embodiment 350 shown in FIG. 3B is similar to the embodiment300 of FIG. 3A, with the exception that the coefficient reorderingprocessor 334 and the block reordering processor 318 are integrated as acombined coefficient and block reordering processor 360, as shown inFIG. 3B. In this embodiment 350, the procedures performed by thecoefficient reordering processor 334 and the block reordering processor318 of FIG. 3A are performed after quantization of the hierarchicallapped transform as a combined step in the embodiment 350 of FIG. 3B.Since the procedures of the coefficient reordering processor 334 and theblock reordering processor 318 of FIG. 3B are performed in an efficientcombined process, the embodiment 350 of FIG. 3B is preferred.

[0055]FIGS. 4A-4B are general block diagrams of decoders related to theencoders of FIGS. 3A and 3B respectively, in accordance with the presentinvention. The decoding embodiments 400, 450 of FIGS. 4A and 4B,respectively, are essentially the inverse of the encoding and datatransformations of FIGS. 3A and 3B, respectively. For the decodingprocess of the embodiment 300 of FIG. 3A, which relates to embodiment300 of FIG. 3A, a bitstream of encoded data 405, such as that producedby the encoder of FIG. 3A, is received at a lossless adaptive decodingprocessor 410. The bitstream 405 may be received directly from thedecoder, from local storage, or from a remote decoder or storage via oneof many viable transmission media such as by removable memory cards,satellite transmission, cable transmission or other network.

[0056] Lossless decoding processor 410 receives the encoded bitstreamand recreates the adaptation rules developed during encoding via a feedforward line 415. Processor 410 essentially receives the string lengthto be used, and reconstructs the data in accordance with the rules.Again, it operates on a block level, but this is not a requirement ofthe invention. It simply makes it more convenient than working with anentire representation of an image or other data all at the same time,which would require a larger amount of memory, or paging if such memorywas not available. One form of fidelity reduction may be performed atprocessor 410 just by not decoding the last bit plane. This effectivelydoubles the step size controlled by the parameter T. It is a simple wayto reduce the fidelity of the data. In general, more bit planes can bedropped, in whole or in part, by processor 410.

[0057] The output of processor 410 should be identical to the integerdata coming out of block 318. However, higher resolution layers of theimage may be removed at this point as indicated, just by effectively notusing higher frequency coefficients. This would be useful if the windowused to display an image or set of images is small. Inverse reorderingprocessor 420 then is used to unshuffle or reorder the blocks back tothe original positions. The output of the inverse reordering processor420 is the integer numbers that need to be remultiplied back at block430 by using a step size that is provided by a header in the receivedbitstream. This provides reconstructed coefficients that closelyapproximate those of the original image data. The header also providesinformation about how big the image size is, and other standard imageformat data. An inverse hierarchical lapped transform 440 is thenperformed by inverse coefficient reordering 442, inverse DCT transform444, and inverse LBT transform 446, which are basically the respectiveinverses of the coefficient reordering 334, DCT transform 332 and LBTtransform 330 of FIG. 3A. It should be noted that the only losses, otherthan selected desired fidelity or resolution reductions, are incurred inthe quantization steps, which is controllable by modification of the Tparameter. Consequently, the decoding scheme 400 produces an outputreconstructed data that substantially matches the input data 310 of FIG.3A.

[0058] The decoding embodiment 450 shown in FIG. 4B relates to theembodiment 350 of FIG. 3B and is similar to the decoding embodiment 400of FIG. 4A. However, the inverse coefficient reordering processor 420and the inverse coefficient reordering processor 442 are integrated as acombined inverse coefficient and block reordering processor 450, asshown in FIG. 4B. In this embodiment 450, the procedures performed bythe inverse coefficient reordering processor 420 and the inversecoefficient reordering processor 442 are performed before beingremultiplied back at block 430, as a combined step.

[0059] The adaptive encoding and decoding of the present inventionoperates very well on data that has clustered zeros with statistics thatchange. This type of data may also be characterized as having a highprobability of data with near exponential decay of the probability oneither side of the zeros. Multimedia data, such as static image data andvideo has this characteristic. Further, the transformation of many typesof physical data also has this type of characteristic. When capturingphysical data, the information normally occurs in just a few places,which means that most of the other data is zero. Symmetry of the data isalso a desired characteristic for this type of encoding to work best. Inother words, an exponential fall off of both negative and positivevalues on either side of an information spike is beneficial. Examples ofsuch physical data include ECGs and other biometric type of data.

[0060] V. Details of the Components and Operation

[0061]FIG. 5A is a block diagram of the hierarchical lapped transform(HLT) processor 500 of the present invention. The HLT processor 500 usesa two-level hierarchical decomposition of both LBT and DCT transformsthat transforms a sample of input pixels to a frequency domainrepresentation. The HLT processor 500 of the present invention producesessentially no blocking artifacts, few ringing artifacts and has a muchlower computational complexity than processors using a lapped orthogonaltransform (LOT).

[0062] In general, the HLT processor 500 cascades LBT blocks to generateLBT coefficients, combines and outputs these LBT coefficients, appliesDCT blocks to a subset of the LBT coefficients (typically thelowest-frequency coefficients) and outputs HLT coefficients forreordering. Reordering of the HLT coefficients is performed to produce aspace-frequency decomposition similar to that of a six-level wavelettransform. This maintains the scalability (in fidelity and resolution)and embedded bitstream features, while greatly reducing thecomputational complexity of the space-frequency decomposition. Inaddition, because the HLT processor 500 preferably uses two-dimensional8×8 DCT blocks, any specialized software or hardware module designed fortwo-dimensional DCT (such as those used in a JPEG codec) can beleveraged by the HLT processor 500.

[0063] The HLT processor 500 includes two decomposition modules: a firstdecomposition module, a LBT module 510, which computes LBT operators anda second decomposition module, a DCT module 520, which computes DCToperators. A DCT decomposition is used in the DCT module 520 (instead ofanother LBT decomposition) because blocking artifacts are alreadyremoved by the LBT module 510. FIG. 5A illustrates a preferredembodiment whereby the HLT processor 500 produces a six-levelspace-frequency decomposition that, as discussed above, is similar to asix-level wavelet transform, but instead uses a HLT.

[0064] As shown in FIG. 5A, a block of input values (such as imagepixels) is received by the LBT module 510 and processed (as discussedbelow) such that groups of LBT coefficients are produced. Some of theseLBT coefficients are, preferably, reordered and sent as output from theHLT processor 500. As shown in FIG. 5A, LBT coefficients X(1) throughX(7) are sent as output from the HLT processor 500. Other LBTcoefficients (in this case, X(0)) are received as input by the DCTmodule 520 and processed. The output of the HLT processor 500 is a blockof HLT coefficients that contain a mixture of LBT operators and DCToperators. For example, in FIG. 5A each HLT block is a cascade of eightconsecutive LBT operators and one DCT operator of length eight. Thus,the HLT processor 500 maps a group of 8 pixel blocks (or 64 pixels) into64 HLT coefficients.

[0065]FIG. 5B is a block diagram of the LBT module 510 of the HLTprocessor 500 of the present invention. In general, the LBT module 510receives an input signal, cascades LBT blocks to generate LBTcoefficients and combines and outputs these LBT coefficients.Specifically, the LBT module 510 receives a vector x(n) containing nsamples of an input signal (such as pixel values) and transforms thevector x(n) into another vector X(N) containing N DCT operators. The LBTmodule 510 generates LBT coefficients for each block by combining DCTcoefficients of adjacent blocks. These LBT coefficients, Y(M), arearranged in groups of odd and even Ms that together represent the LBTcoefficients of a block. It should be noted that, in thisimplementation, N=M=8, such that the input signal vector (x(0) to x(7))produces the DCT operators (X(0) to X(7)) and corresponding LBTtransform vectors (Y(0) to Y(7)) as an output to the DCT module 520.

[0066] As discussed further below, the LBT module 510 generates LBTcoefficients for each block using mainly +1/−1 butterfly operators.Scaling factors {a,b,c} control the shape of the basis functions, and aslong as inverse scaling factors {1/a,1/b,1/c} are used in the inversetransform, the transform is guaranteed to be biorthogonal. This meansthat in the absence of quantization (which introduces lossy effects) theinput data is recovered exactly by the inverse transform. The additionalscaling factors b and c allow the coding gain to be maximized, assumingthat all coefficients are quantized with the same step size. One exampleof scaling factors {a,b,c} that may be used with the LBT are given inTable 1. TABLE 1 Example scaling factors for the LBT. Parameter DirectTransform Inverse Transform a {square root over (2)} {square root over(1/2)} b {square root over (3/4)} {square root over (4/3)} c {squareroot over (4/5)} {square root over (5/4)}

[0067] The operator Z 530 is an orthogonal matrix that is used tocontrol the shape of the odd basis functions. As can be seen from FIG.5B, there is overlapping across consecutive blocks that helps eliminateany blocking artifacts. It should be noted that FIGS. 5A and 5Billustrate one way in which the operation of the HLT processor 500 maybe implemented, and those skilled in the art will recognize numerousother implementations that may be used.

[0068]FIG. 6 is a flow diagram of the hierarchical lapped transformprocessor of FIG. 5A of the present invention. In general, the HLTprocessor 500 first receives input data, such as pixel data (box 610), afirst stage generates LBT operators from the pixel data (box 612). Thefirst stage (box 612), which is a flow diagram of the LBT processor ofFIG. 5B, includes a first sub-stage (box 614), a second sub-stage (box616) and a third sub-stage (box 618). The first sub-stage (box 614)computes DCT operators for each input pixel block. The second sub-stage(box 616) performs cascading butterfly operations with window functionson the DCT operators and the third sub-stage (box 618) performsadditional cascading butterfly operations and orthogonal operations onthe DCT operators to control the shape of the odd basis functions.

[0069] The input data is mapped to a cascade of butterflies using afirst set of weights and the cascade of butterflies is reordered. Thefirst stage (box 612) produces blocks of LBT coefficients (box 620) fora second stage that produces DCT operators (box 622) for generatinghierarchical coefficients lapped biorthogonal coefficients (box 624) forreordering (box 628). Namely, a spatial transform is computed from thereordered cascade of butterflies to produce the hierarchicalcoefficients lapped biorthogonal coefficients.

[0070] The pixel data can be processed by rows and then by columns andresults in a two-dimensional transformation. Preferably, the HLBT can becomputed by successfully processing overlapping blocks of M×N (typically64) pixels. In the row/column approach, the rows and columns areprocessed in two steps. For instance, first, a set of LBTs of length Ncan be computed and then a set of DCTs of length M can be computed. Inone example, N=M=8, however, other choices are possible. For example, Nand M can be chosen so that they are powers of 2 (such as 2, 4, 8, 16and so forth) to make the computation of transforms faster. Generally,the values of N and M would be increased for a very large image (such asan image containing more than 2,000 by 2,000 pixels).

[0071] VI. Working Example

[0072]FIG. 7 is a working example represented by a flow diagramillustrating the detailed operation of the components of thehierarchical lapped transform (HLT) processor 500 of FIGS. 5 and 6. TheHLT processor 500 begins and reads a buffer containing pixel data. Inthis example, the data within the buffer is grouped into K blocks oflength N. The LBT module 510 takes the data within the buffer one blockat a time (by setting a pointer) and computes K LBT transform blocks andLBT operators for the data pointed to by the pointer.

[0073] Next, in box 710, a number of DCT operators, L, is determined bydividing the number of blocks K by the number of DCT coefficients M. Inaddition, a vector u of length M is allocated in memory to receive thecomputed DCT coefficients. The HLT processor 500 then proceeds to theDCT module 520 where the DCT operators are computed and used toconstruct the vector u. In loop of box 720, a block is selected and aloop of box 730 is entered whereby the vector u is filled with every NthLBT coefficient computed earlier. The DCT transform of every Nth LBTcoefficient is determined in box 740. In box 750, each of the DCTcoefficients computed in box 740 are used to construct the vector u. TheDCT operators and the LBT operators are then stored in memory. Together,the DCT operators and the LBT operators make up the HLT coefficientsthat are sent as output from the HLT processor 500.

[0074]FIG. 8 is the working example of FIG. 7 representing a flowdiagram illustrating detailed operations of the LBT module 510 of FIG.7. In general, the LBT module 510 includes a DCT operator module 810,which computes DCT operators for each input pixel value, a firstbutterfly operator module 820, which performs butterfly operations onthe DCT operators, and a second butterfly module 830 that performsadditional butterfly operations and orthogonal operations on the DCToperators.

[0075] The working example of FIG. 8 begins by reading an input buffercontaining blocks of image sample (or pixels). The DCT operator module810 receives this data as input and computes DCT operators for the datain each block. If the block is a first block the DCT operator module 810uses a scaling factor a to control the shape of the basis functions. Thecomputed DCT operators (except for the first block) are sent to thefirst butterfly operator module 820. The first butterfly operator module820 computes +1/−1 butterflies for each DCT operator within each of theblocks. This data is received by the second butterfly operator module830 in addition to the first block and for each of the blocks additionalbutterfly operations are performed. In addition, the second butterflyoperator module 830 uses additional scaling factors b and c to furthercontrol the shape of the basis functions. Further, an orthogonaloperator Z is used on the odd basis functions to control their shape.The computed LBT coefficients are sent as output from the LBT module510.

[0076]FIG. 9 is the working example of FIG. 7 represented by a blockdiagram illustrating a first reordering of HLT coefficients. This firstreordering is used to have the space-frequency relationships of the HLTcoefficients for each N×N LBT block more closely approximate those ofwavelet coefficients. Although HLT coefficients produced by the HLTprocessor 500 generate a multiresolution decomposition, this firstreordering is performed to approximate the time-frequency decompositionachieved with wavelet transform coefficients. The first reorderingoccurs according to the matrix shown in FIG. 9, where, in this workingexample, N=8.

[0077] The diagram of FIG. 9 indicates that if there are HLTcoefficients numbered in a row-scan order (i.e., [0 1 2 3 4 5 6 7] inthe top row, [8 9 10 11 12 13 14 15] in the second row, and so forth),the HLT coefficients should be reordered as shown in FIG. 9. Moreover,the DCT operators of the HLT coefficients are further processed with theDCT operators, which occurs independent of the HLT reordering shown inFIG. 9. Thus, HLT reordering may be performed either before or aftercomputation by the DCT module 520.

[0078]FIG. 10 is a working example represented by a block diagramillustrating reordered HLT coefficients produced by the reordering andblocking module of FIG. 3A. A second reordering is performed inaccordance with FIG. 10 to cluster any insignificant values. In FIG. 10,each number within the figure represents the scanning order of a blockof M_(B)×N_(B) HLT coefficients. The reason for the alternate scanningof the low-high (LH) and high-low (HL) HLT coefficients within the sameresolution level is simple. Assuming the original image has a particularfeature (or no feature) at some spatial location, it is likely thatclusters of both the LH and HL subbands, corresponding to that location,will have large (or small) values. Therefore, by ensuring that pairs ofblocks from the LH and HL subbands corresponding to the same spatiallocation appear contiguously in a macroblock or at least proximate orclose to each other, we're more likely to create clusters of large andsmall values. That increases the probability of long runs of zeros inthe bit planes of the quantized coefficients.

[0079]FIG. 11 is a working example represented by a flow chart showingthe general operation of the lossless adaptive coefficient encoder ofFIG. 3A, which separates the coefficients into bit planes and encodesthem using an adaptive run-length encoder. The process begins (box 1105)and the bit planes are read from an input buffer x (box 1110) thatcontains N numbers. The number of bit planes, bmax, is computed (box1115) and a significance flag vector, sflg, is set to all zeros (box1120). Encoding begins with the most significant bit plane and a bitplane index variable bit is set equal to bmax (box 1125). The values ofthe bits pointed to by the index “bit” form the bit plane vector bp (box1130). For each plane bp, the bits are divided into two subsets (box1135 and box 1140. A significant bits, x1, corresponds to positions forwhich a “1” entry has not been seen in the higher planes. A refinementbit, x2, corresponds to positions for which a “1” entry has already beenseen in the higher planes.

[0080] Next, x1 is encoded with the adaptive run-length+Golomb-Rice(ARLGR) encoder (box 1145) that benefits from a higher frequency ofzeros in x1. For every bit equal to 1 in x1, the sign bit is alsoencoded and appended at the end of the output code. Straight binaryencoding is then used to encode x2 (box 1150). This is performed byappending the x2 bits to the output stream. Minimal loss in encodingefficiency is encountered because zeros and ones are usually equallylikely in x2. It should be noted that the sign bits are not referred toas a bit plane because they are not processed as a bit plane. The signbits are sent in the process of coding the x1 vectors of each bit plane.Therefore, the vector x1 can be thought of as being drawn from thealphabet {0, +1, −1}, i.e. bit plus sign.

[0081] An important property of the flow chart in FIG. 11 is that theinformation on which are the bits that belong to x1 and which are thebits that belong to x2 does not need to be explicitly encoded. Thevector sflg controls the allocation of bits to x1, and sflg is firstinitialized to all zeros, and then updated after each bit plane isencoded (box 1155). Thus, the decoder can easily track the changes tosflg. Continuing to the next bit plane, a bit is decremented (box 1160)and checked to determine if the last plane has been decoded (box 1165).If not, control is passed to box 1130 for encoding of the next bitplane. If bit was equal to zero, or a higher number of a lowerresolution encoding is desired, an output buffer containing outputs ofall x1 and x2 encodings is written (box 1170) and the process ends (box1175).

[0082] In the present invention, the Golomb-Rice codes for a source ofbinary digits are combined with RL codes. This results in aRun-Length+Golomb-Rice (RLGR) code, which is characterized by aparameter k that controls the length of the run associated to thecodeword 0 (where the maximum run length is equal to 2^(k)). For a givensource of input vectors, using either the {0,1} or the {0,+1,−1}alphabets, the parameter k should be chosen in order to minimize theexpected code length. If the source has no memory, has constantstatistics over time, and is characterized by P₀=Prob{symbol=0}, then itis easy to compute the optimal value of k as a function of P₀.

[0083] In practice, however, binary (or binary + sign) vectors are notstationary. Typical examples include data obtained from the physicalworld, such as quantized wavelet coefficients of pictures or scanneddocuments. Therefore, we need to adjust the RLGR parameter k over time,to best match the local statistics of the data. Many strategies havebeen considered, mostly involving dividing the input data in blocks ofappropriate length. For each block, P₀ is estimated and then the optimalvalue of k is computed. An additional code is then sent at the beginningof each block to indicate the value of k that should be used by thedecoder.

[0084] The coefficient encoder of the present invention uses abackward-adaptive strategy for changing the RLGR parameter k. Bybackward-adaptive, it is meant that variations in k are computed basedon encoded symbols, not directly on the input data. The basic strategyis that the value of k to be used in encoding the next symbol shoulddepend only on previously encoded data. Therefore, all the decoder needsto do to recover the changing values of k is to apply the sameadaptation rule as the encoder. Therefore, to simplify decoding it isimportant that such a rule be as simple as possible to compute.

[0085] The adaptive Run-Length+Golomb-Rice (ARLGR) encoder of thepresent invention uses the following rules for changing the parameter k.FIG. 12 is a working example represented by a flow chart illustratingfurther detail of the working example of the adaptiverun-length+Golomb-Rice encoder of FIGS. 11 and 3A. The process starts(box 1202) with defining several parameters (block 1204). A scale factorL is first defined and is used to define kp as L*k. kp is an auxiliaryparameter whose value moves up or down by an amount Up or Dnrespectively to permit fractional moves of k without the use offloating-point arithmetic. Finally, Uq is defined and used to move kp upif the output code was zero and k was equal to zero.

[0086] An input buffer x is read (box 1206) and contains M numbers.Next, k is set to k0, kp is set to L*k and run is set to 0 (box 1208).The process is started with a value of k that is a good choice for thelong-term statistics of the incoming data, e.g. k=2. Starting with thefirst symbol, xindex=1 (box 1210), symbol is set to x(xindex) and runmaxis set to 2^(k) (box 1212).

[0087] As an overview of the encoding process, after encoding a sourcesymbol, kp is adjusted based on the emitted output code. If the outputcode was 0 and k≠0, kp is incremented by a predefined increment step Up,i.e. set kp=kp+Up. If the output code was 0 and k=0, kp is incrementedby a predefined increment step Uq, i.e. set kp=kp+Uq. If the output codestarted with a 1 (corresponding to a nonzero input), kp is decrementedby a predefined decrement step Dn, i.e. set kp=kp−Dn. The value of k forencoding the next input symbol is set to k=┌kp/L┐ (i.e. truncate kp/Ldown to the nearest integer.

[0088] The algorithm is based in a simple strategy. If a run of zeros isencountered, k is increased to allow for longer sequences of zeros to becaptured by a single output bit=0. If a nonzero symbol is encountered, kis reduced to avoid excessively long output codes. The use of theauxiliary parameter kp and the scale factor L above allows adjustment ofk in fractional steps without having to use floating-point arithmetic asindicated above. For most of the data tested in the ARLGR encoder, theperformance was quite good (encoded rates very close to sourceentropies), for the following typical choice of parameters: L=4, Up=4,Dn=5, and Uq=2. In some cases, adjustments on these parameters can leadto slightly better performance.

[0089] Returning to the description of the flowchart in FIG. 12,following initialization and defining of parameters, k is checked (box1214) to see if it is equal to zero. If it is, and if symbol is zero, Uqis added to kp (box 1218). A zero is appended to the output buffer (box1220) and if kp is out of range (above kpmax then it is clipped (box1222). Next, k is set to the largest integer less than kp/L, the scalefactor (box 1224). Xindex is then incremented (box 1226), and if lessthan M (box 1228) the next symbol is selected (box 1212). If greaterthan M, the output bit buffer is written to (box 1230) and the processends (box 1240).

[0090] Referring back to decision block 1216, if symbol was not equal tozero, a 1 is appended to the output bit buffer (box 1242) and a sign bitof symbol is appended to the output bit buffer (box 1244), andprocessing continues (box 1222) to check to see if kp is within range.If k is not equal to 1 (box 1214), a further check of symbol isperformed (box 1250). If symbol is not equal to zero, a 1 is appended tothe output bit buffer (box 1252) and a k-bit value of run is appended tothe output bit buffer (box 1254). Next, Dn is subtracted from kp (box1256) and processing continues whereby an optional sign bit is appended(box 1244).

[0091] If symbol is found to be zero at box 1250, run is incremented(box 1260) and then checked (box 1262) to see if it is equal to runmax.If not, kp is clipped to not exceed kpmax (box 1222). If run was equalto runmax (box 1262), a zero is appended to the output bit buffer (box1264) and run is set to zero (box 1266). Finally, Up is added to kp, andprocessing again reverts to block 1222 for clipping of kp, setting of k(box 1224), incrementing xindex (box 1226) and checking to see if thelast symbol has been processed (box 1228). If so, the information iswritten to the output bit buffer (box 1230) and the process is ended(box 1240).

[0092] A more detailed description of the techniques described in FIGS.11 and 12 can be found in the following co-pending U.S. patentapplications: (1) Ser. No. 09/276,954, filed on Mar. 26, 1999, entitled“Image Encoding Using Reordering and Blocking of Wavelet CoefficientsCombined with Adaptive Encoding” by Henrique Malvar; and (2) Ser. No.09/277,255, filed on Mar. 26, 1999, entitled “Lossless Adaptive Encodingof Finite Alphabet Data” by Henrique Malvar. The subject matter of bothpatent applications is hereby incorporated by reference in theirentirety.

[0093]FIG. 13 is a working example represented by a flow chartillustrating the writing of a matrix of coefficients in a reorderedmanner consistent with the block reordering map shown in FIG. 10. Thisflowchart in describes an algorithm used to write the blocks ofcoefficients in the order shown in FIG. 10. The algorithm may beimplemented in computer program instructions, or in hardware, firmwareor a combination of all as desired.

[0094] Referring to FIGS. 10 and 13, the algorithm is entered (box 1310)and an input matrix Q containing M×N quantized HLT coefficients is read(box 1315). A number of HLT levels is defined (box 1320) in a knownmanner as JW. A block size is defined (box 1325) as NH×NV, with NH equalto MI(2^(JW)) and NV equal to NI(2^(JW)). The first output block is thenwritten (box 1330) and IH and IV are initialized as NH and NVrespectively for use in defining loops for writing of further blocks,which are larger in size. For a simplified example, assume that in FIG.10, the matrix Q is 16 by 16, with 4 HLT levels, and a block size of 1.This provides an initial IH and IV of 1. In further examples, the blocksize may be larger, such as 8×8 or 16×16, or even higher. Also, theblocks do not need to be square (i.e. NH may be different from NV. Thistypically happens when handling input images that are not square).

[0095] A decision block (box 1340) is used to determine whether theentire matrix of HLT coefficients has been written by checking to see ifIH is less than M. If IH is still less than M, more HLT coefficientsneed to be written. As seen in FIG. 10, the first blocks of HLTcoefficients are of dimension 1 by 1, and then they increase to 2 by 2,4 by 4 and so forth. The next sets of flowchart blocks are used to writethe succeeding blocks by looping from one to a block size parameter NBLKthat is set (box 1345) as IH/NH. A nested loop using I (box 1350) andusing J (box 1355) is used to control the order of writing of the outputblocks LH and HL (box 1360). J is incremented at a first NEXT statement(box 1362), while I is incremented at second NEXT statement (box 1364).This results in rows of the blocks being written first in thisparticular implementation. Columns may also be written first if desired,or any other order of writing may be used. For the first time throughthe loop, given a matrix of size 16 by 16 and 4 levels, NBLK is also 1,so only blocks 1030 and 1040 are written.

[0096] Following the writing of the next LH and HL blocks, a second setof nested loops is set up again using I (box 1370) and using J (box1375) to define positions in which to write an output block (box 1380).This output block corresponds to HH blocks at the same level, which isblock 1050 for the first time through. A first NEXT statement for J (box1382 and a second NEXT statement for I (box 1384) complete the nestedloop. It should be noted that the HH block could also have been writtenat the same time as the LH and HL blocks above since the nested loopsare identical. After all the blocks at this level have been written, IHand IV are incremented as exponents of 2 (box 1390) and then compared(box 1340) to see if IH is still less than M. If IH is not less than M,the algorithm is exited (box 1395) after having provided at completereordered set of HLT coefficients in accordance with the presentinvention.

[0097] The second time through the nested loops, blocks 1055, 1060 and1070 are written, followed by blocks 1080, 1075 and 1090 the third timethrough the nested loops. Larger matrix sizes with higher levels arealso possible. To recover the original order for decoding purposes, theoutput of the reordering algorithm is read in the same manner in whichit was written. All that is required is knowledge of the size of theoriginal matrix, and the number of levels that were written. Then thewriting order is simply reversed to provide the coefficients in theoriginal order. A more detailed description of the techniques describedin FIGS. 10 and 13 are discussed in co-pending U.S. patent applicationSer. No. 09/280,135, filed on Mar. 26, 1999, entitled “ReorderingWavelet Coefficients for Improved Encoding” by Henrique Malvar, thesubject matter of which is hereby incorporated by reference in itsentirety.

[0098] VII. Real World Implementation

[0099]FIG. 14 is a simplified block diagram illustrating a real worldimplementation of the encoder of FIGS. 3A-3B and the decoder of FIGS.4A-4B in a software application environment 1410 that handles imagedata. In particular, the software application environment 1410 includesa plurality of high-level application environments 1420 such as e-mail,word processing, spreadsheet, intent browser presentation and othertypes of applications. This application environment level 1420 issupported by at least two lower levels that provide software functions,hardware functions or a combination of both. The two lower levelfunctions include a facsimile/scanner function 1430 and a videoinput/output function 1440. In addition, several other types offunctions may reside at this level.

[0100] The video input/output function 1440 provides the ability todisplay and receive video and image data from external sources. Thevideo input/output function 1440 and the facsimile/scanner function 1430use the encoder and decoder of the present invention 1450 to provideencoding and decoding functions as described above. If raw image orother suitable data is captured (such as in pixel or other form) theencoder 1450 may be used to encode the data. Moreover, if data encodedusing the type of encoding of the present invention is received from anysource the decoder 1450 may be called by the high-level applicationenvironment 1420 to transform of decode the data into a displayable orusable format.

[0101] Many applications that comprise an integrated suite of softwareapplications (such as several software applications that work inconjunction) may need to share files easily with each other and arelikely to deal with data that needs to be compressed or decompressed.The present invention provides compression that is free from blockingartifacts (such as those present in JPEG) and is less complex toimplement in software, hardware or a combination of both. For example,software or hardware (such as digital cameras, printers and Internetappliances) that are designed to use JPEG compression can more easilyimplement the present invention. Moreover, the present inventionprovides single-pass encoding for any desired compression ratio as wellas scalability. This means that an image that has been encoded at acertain fidelity may be decoded at a lower fidelity, thereby allowing,for example, a server to distribute different versions of the sameencoded image to different clients having different capabilities.

[0102] The foregoing description of the invention has been presented forthe purposes of illustration and description. It is not intended to beexhaustive or to limit the invention to the precise form disclosed. Manymodifications and variations are possible in light of the aboveteaching. It is intended that the scope of the invention be limited notby this detailed description, but rather by the claims appended hereto.

1-17. (Canceled)
 18. A method of encoding transform coefficientscorresponding to image data, comprising: generating the transformcoefficients using a transform; and reordering the transformcoefficients in a data-independent manner to group similar image data.19. The method of claim 18, wherein the transform coefficients are ahierarchical multiresolution representation of the image data.
 20. Themethod of claim 19, wherein the transform coefficients are generatedusing a lapped biorthogonal transform and a discrete cosine transform.21-31. (Canceled)
 32. The method of claim 18, further comprisinggenerating the transform coefficients using a hierarchical transform.33. The method of claim 18, further comprising encoding the reorderedtransform coefficients.
 34. The method of claim 33, further comprisingencoding the reordered transform coefficients using an adaptiverun-length encoder.
 35. The method of claim 34, further comprisingencoding the reordered transform coefficients using a backward-adaptiverun-length encoder.
 36. A method of encoding digital data, comprising:generating coefficients corresponding to the digital data; reorderingthe coefficients using a data-independent technique to generategroupings of coefficients having similar values.
 37. The method of claim36, further comprising generating the coefficients using a hierarchicaltransform.
 38. The method of claim 37, further comprising encoding thereordered coefficients.
 39. The method of claim 36, wherein thedata-independent technique further comprises fixing a scanning order ofthe coefficients.
 40. The method of claim 39, further comprisingclustering coefficients having insignificant values.
 41. A method ofcompressing a digital signal, comprising: generating transformcoefficients of the signal using a hierarchical transform; andreordering the transform coefficients in a data-independent manner suchthat data-dependent data structures are not used.
 42. The method ofclaim 41, further comprising clustering coefficients havinginsignificant values.
 43. The method of claim 41, wherein no waveletsare used in the compression of the digital signal.
 44. The method ofclaim 41, wherein reordering the transform coefficients in adata-independent manner further comprises reordering transformcoefficients having large values and transform coefficients having smallvalues into separate groups.
 45. The method of claim 44, furthercomprising encoding the reordered transform coefficients using abackward-adaptive run-length encoder.